SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road QUESTION BANK (DESCRIPTIVE)

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1 QUESTION BANK 8 SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayaavaam Road 5758 QUESTION BANK (DESCRIPTIVE) Subject with Code : (6HS6) Course & Brach: B.Tech AG Year & Sem: II-B.Tech& I-Sem Regulatio: R6 UNIT I COMPLEX ANALYSIS-I.. A) Show that w log dw is aalytic everywhere ecept at the origi ad id. d B) I is the aalytic uctio o prove that log. A) Show that u y is Harmoic. B) Fid the aalytic uctio whose imagiary part is e y ycos y log. A) Determie p such that the uctio y y. si. i ta B) Fid all the values o k, such that e cos kyisi ky p. y. 4. A) I u iv is a aalytic uctio o ad i u ve cos ysi y, Fid i terms o. B) Fid a aalytic uctio whose real part is e si y y cos y. 5. A) Show that () = + is ot aalytic aywhere i the comple plae. B) Show that 4. y y where c cosists o the lie segmets rom 6. A) Evaluate the lie itegral i to i B) Evaluate 7. A) Evaluate B) Evaluate c c c c d ad the other rom to i. cos si d with C : usig Cauchy s itegral ormula. i e d i where c is the circle usig Cauchy s itegral ormula. d where c is the circle usig Cauchy s itegral ormula. 4 6HS6

2 QUESTION BANK 8 i 8. Evaluate iy d alog the paths i y ii y. [M] 6 9. A) Evaluate usig Cauchy s itegral ormula si d aroud the circle c B) Evaluate c log d c :. where c : usig Cauchy s itegral ormula.. Let C deote the boudary o the square whose sides lie alog the lies = ±, Where c is e cos described i the positive sese, evaluate the itegrals ( i) d ( ii) c i d [M] 8 c Prepared by: RAJAGOPAL REDDY N 6HS6

3 QUESTION BANK 8 SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayaavaam Road 5758 QUESTION BANK (OBJECTIVE) Subject with Code : (6HS6) Course & Brach: B.Tech AG Year &Sem: II-B.Tech& I-Sem Regulatio: R6 UNIT-I ) I () = or all the () is A) Cotiuous at = i B) Not Cotiuous at = i C) Cotiuous at = D) Noe ) I = + iy the si = A) si coshy cos si hy B) si coshy + i cos si hy C) si coshy + cos si hy D) si coshy i cos si hy ) I () = is A) Aalytic everywhere B) ot aalytic everywhere C) Not dieretiable at = D) Noe 4) Cauchy-Riema equatios are A) u = v y & u y = v B) u = v y & u y = v C) u = v & u y = v D) u = v y & u y = v 5) The period o si is A) B) C) π D) π 6) Fuctios which satisy Laplacia equatios i a regio are called A) aalytic B) ot aalytic C) Harmoic D) Noe 7) A aalytic uctio with costat modulus is a A) costat uctio B) uctio o C) uctio o y D) Noe 8) Imagiary part o cos is A) si coshy B) si si hy C) si hy coshy D) cos coshy 9) si i = A) isi hy B) si hy C) icos hy D) isi hy ) The value o k so that + + ky may be harmoic is A) B) C) D) oe ) I w = log is aalytic everywhere ecept at = A) B) C) D) ) I = + iy the cos = A) si coshy cos si hy B) cos coshy i si si hy C) cos coshy + cos si hy D) si coshy i cos si hy ) The value o k so that + ky may be harmoic is A) B) C) D) oe 6HS6

4 QUESTION BANK 8 4) I () is aalytic uctio i a simply coected domai D&C is ay simple Curve the (Z)d = A) B) C) D) oe 5) The curves u(, y) = C ad v(, y) = C are orthogoal i u + iv is A) aalytic B) ot aalytic C) Harmoic D) Noe 6) I u + iv is aalytic the v iu is A) aalytic B) ot aalytic C) Harmoic D) Noe 7) A harmoic uctio is that which is A) Harmoic B) ot aalytic C) aalytic D) Noe 8) A aalytic uctio with costat imagiary part is A) costat B) aalytic C) Harmoic D) Noe 9) I () is aalytic ad equals u(, y) + iv(, y) the () = A) u + iv B) v y iv C) v y + iv D) oe ) cos i = A) isi hy B) si hy C) icos hy D) cos hy ) The period o si is A) B) C) π D) π Lt eists the that limit is ) I A) Not uique B) Uique C) Twice D) Noe ) Solutio set o si is A) B) D) Noe C) 4) I = + iy the cos A) cos B) si C) cos D) Noe 5) Imagiary part o si A) si coshy B) si si hy C) si hy coshy D) cos sih y is 6) I A) Aalytic everywhere B) ot aalytic everywhere C) Not dieretiable at = D) Noe 7) Arg is A) Dieretial i every domai B) Not dieretial ay where C) Dieretial oly at origi D) Noe 8) Polar orm o Cauchy-Riema equatios are r u v, r v u B) r ur v, r vr u v, r vr u D) r ur v, r vr u A) r r r u C) r is A) Not dieretiable at = B) ot aalytic everywhere C) Aalytic everywhere D) Noe 9) I 6HS6

5 QUESTION BANK 8 ) Real part o cos is A) si coshy B) si si hy C) si hy coshy D) cos coshy ) The period o ta is A) B) C) π D) π ) I Re is A) aalytic B) ot aalytic C) ot dieretiable D) Noe ) A poit at which () ails to be aalytic is called A) Sigular poit o () B) ull poit o () C) No-Sigular poit o () D) oe 4) I sih is A) ot aalytic everywhere B) Aalytic everywhere C) Not dieretiable at = D) Noe 5) The period o the uctio is A) B) C) π D) π si e i 6) I = + iy the A) B) si C) cos D) Noe 7) Solutio set o cos is A) B) D) Noe si C) y 8) sih sih A) B) - C) D) y 9) I si i iy the si cos A) B) - C) D) 4) I e A) B) e C) D) e Prepared by: RAJAGOPAL REDDY N 6HS6

6 QUESTION BANK 8 SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayaavaam Road 5758 QUESTION BANK (DESCRIPTIVE) Subject with Code : (6HS6) Course & Brach: B.Tech AG Year & Sem: II-B.Tech& I-Sem Regulatio: R6 UNIT II COMPLEX ANALYSIS-II ad the residues at each pole 4 where c is.. A) Determie the poles o the uctio B) Fid the residue o the uctio i. A) Fid the residues o 4 at these sigular poits which lie iside the circle B) Fid the residues o a at.. A) Determie the poles o the uctio ad the residues at each pole. B) Determie the poles ad residues o ta h. cos a 4. A) Evaluate d, a o. e B) Fid the residue o the uctio where C :. ai 5. Evaluate d,, a b. [M] a bcos a b cos a 6. Show that d,, a acos a a usig residue theorem. 5 [M] 7. A) Fid the biliear trasormatio which maps the poit s (, i, ) i to the poits(, i, ) B) Fid the biliear trasormatio that maps the poit s (,, i) i to the poits + i, i, i i W-plae 8. A)By the trasormatio w, show that the circles a c Z-plae correspods to the limacos i the w-plae. B) Fid the image o the regio i the -plae betwee the lies trasormatio (a, c beig real) i the y & y uder the w e. 6HS6

7 QUESTION BANK 8 9. A)Fid the biliear trasormatio which maps the poits (, i, ) i to the poits (,, ) i w-plae. B) Fid the biliear trasormatio that maps the poit s (, i, ) i to the poits (, i, ) i w-plae. A) The image o the iiite strip bouded by & uder the trasormatio 4 B) Prove that the trasormatio w = si maps the amilies o lies = y = costat ito two amilies o coocal cetral coics. w cos Prepared by: RAJAGOPAL REDDY N 6HS6

8 QUESTION BANK 8 SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayaavaam Road 5758 QUESTION BANK (OBJECTIVE) Subject with Code : ENGINEERING MATHEMATICS (6HS6) Course & Brach: B.Tech AG Year &Sem: II-B.Tech& I-Sem Regulatio: R6 Lt ) I a UNIT-II COMPLEX ANALYSIS-II does ot eist the is sgularity a A) Pole B) Removable C) Isolated essetial D) Noe ) The uctio has a isolated sigularity at = A) B) C) D) Noe ) The limit poit o a sequece o poles o a uctio () is A) Pole B) Removable C) Isolated essetial D) Noe e 4) The value o d, C : is c A) B) C) D) Noe e 5) The pole o () = e is ()(+) A), B), C), D), 6) The pole o () = is ( )( ) A), B), C), D), + 7) The pole o () = is ( )( ) A), B), C), D), 8) The residue o () = ( +4) at the pole = i is i A) i B) i C) i D) i 9) The residue o () = 4 at the pole = is A) 4 B) 4i C) 4 D) 4 ) A pole o order is called A) Simple B) Not simple C) Isolated D) Noe Lt the ) I a a eists is A) Pole B) Removable C) Isolated D) Noe Lt eists iitely the ) I a a is sgularity A) Pole B) Removable C) Isolated D) Noe 6HS6

9 ) The value o 4) The pole o c d d, 5) The residue o 6) I C : QUESTION BANK 8 is A) B) C) D) Noe e is 4 A),-4 B),4 C),-4 D) -4,- e at the pole = is 4 A) B) 4 C) D) has a simple pole at the Re s a a A) B) Lt a a i C) Lt a a D) Noe 7) Is cross ratio o our poits ivariat uder the trasormatio is A) Biliear B) Iverse Biliear C) coormal D) Noe 8) The image o the lie y c uder the mappig w si is A) Parabola B) ellipse C) Hyperbola D) Noe 9) The cross ratio o the our poits,,, 4 is A) B) C) D) Noe 4 4 ) The biliear trasormatio maps iverse poits o a circle ito A) Iverse poits B) costat C) sigular poit D) Noe ) The image o the lie y c uder the mappig w cos is A) Parabola B) ellipse C) Hyperbola D) Noe ) The type o sigularity o the uctio e at i is A) Simple pole B) Not simple pole C) Isolated essetial D) Noe si ) At has a sigularity at which is called A) Simple pole B) Not simple pole C) Isolated essetial D) Removable 4) The residue o e at the pole = is A) B) - C) D) Noe 5) The image o the lie k uder the mappig w si is A) Parabola B) ellipse C) Hyperbola D) Noe 6) The pole o is 4 A),-4 B),4 C),-4 D) -4,- 4 6HS6

10 QUESTION BANK 8 7) Uder the trasormatio is coormal everywhere ecept at A) Etire w-plae B) Origi C) Iiite strip D) Noe 8) The type o sigularity o the uctio si at is A) Simple pole B) Isolated essetial C) Not simple pole D) Noe si 9) has a sigularity at which is called A) Simple pole B) Not simple pole C) Isolated essetial D) Removable ) The image o the lie k uder the mappig w cos is A) Parabola B) ellipse C) Hyperbola D) Noe ) The pole o w 4 is A),-4 B),4 C),-4 D) -4,- ) I has a simple pole at Re s a the a A) B) Lt a a ) I has a simple pole at the s A) B) Lt d 4) The value o d, 5 5) The residue o c C) Lt a a D) Noe Re C) Lt D) Noe C : is i A) B) C) D) Noe at the pole ia is a ia A) B) C) 6) The pole o A) i 7) The pole o ia a ia D) is c 4 d B),i C) D) Noe is A),4,- B),-4, C),4, D),-4,- a b 8) The biliear trasormatio w is coormal i c d A) ad bc B) ad bc C) ab cd D) ab cd 9) The pole o is 4 A) i B),i C) D) Noe b d 4) I ad bc the the every poit o -plae is a a c A) Iverse poits B) Critical poits C) sigular poit D) Noe Prepared by: RAJAGOPAL REDDY N 6HS6

11 QUESTION BANK 8 SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayaavaam Road 5758 QUESTION BANK (DESCRIPTIVE) Subject with Code : (6HS6) Course & Brach: B.Tech AG Year & Sem: II-B.Tech& I-Sem Regulatio: R6 UNIT III. Fid a positive root o correct to two decimal places by bisectio method.. Fid out the square root o 5 give., 7. usig bisectio method. [M]. Fid out the root o the equatio ( ). usig alse positio method. [M] log 4. Fid the root o the equatio usig Regula-alsi method. [M] 5. Fid a real root o the equatio e cos usig Newto- Raphso method. [M] 6. Usig Newto-Raphso Method A) Fid square root o. B)Fid cube root o 7. [M] 7. From the ollowig table values o.ad.8 [M] e y ad y = ta iterpolate values o y whe 8. A) Usig Newtos orward iterpolatio ormula., ad the give table o value () Obtai the value o () whe =.4 B) Evaluate () give () = 68,9,6at =,7,5 respectively, use Lagrage Iterpolatio. 9. A) Use Newto s Backward iterpolatio ormula to id () give(5) =.77, () =.7 (5) =.86, (4) =.794 B) Fid the uique polyomial P(X) o degree or less such that P() = P() = 7, P4 = 64 usig Lagrage s iterpolatio ormula.. A) Usig Lagrage s iterpolatio ormula, id the parabola passig through the poits (,),(,) ad (,55) B) For =,,,,4 ; (X) =,4,5,5,6 id () usig orward dierece table. Prepared by: RAJAGOPAL REDDY N 6HS6

12 QUESTION BANK 8 SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayaavaam Road 5758 QUESTION BANK (OBJECTIVE) Subject with Code : (6HS6) Course & Brach: B.Tech AG Year &Sem: II-B.Tech& I-Sem Regulatio: R6 UNIT-III ) Eample o a trascedetal equatio A. log. B. C. 7 D. Noe ) I irst two approimatio ad are roots o 9 are ad by Bisectio method the is A..5 B..5 C..5 D..5 ) Eample o a algebraic equatio A. log. B. C. ta D. Noe 4) I case o Bisectio method, the covergece is A. liear B. C. very slow D. quadratic 5) Bisectio method is used or A. Solutio o algebraic or trascedetal equatio B. Itegratio o a uctio C. Dieretial o a uctio D. Solutio o a uctio 6) For method o solutio o equatios o the orm () = approimatio is to be very close to the root ad ( ) A. Bolao B. Newto-Raphso C.Secet D. Chord 7) I the two roots are & o 4 by Bisectio method the A..5 B..5 C..5 D..5 8) Eample o a trascedetal equatio A. ce ce B. 7 C. 5 7 D. Noe 9) I irst two approimatio ad are roots o log 7 are.5 ad 4 by Bisectio method the is A..75 B..75 C..75 D ) I irst two approimatio ad are roots o 9 are ad by Bisectio method the is A..5 B..5 C..5 D..5 ) I irst two approimatio ad are roots o 4 are ad by Bisectio method the is A..5 B..5 C..5 D..5 is 6HS6

13 QUESTION BANK 8 ) The order o covergece i Newto-Raphso method is A. B. C. D. ) The Newto-Raphso method ails whe A. is egative B. is ero C. is too large D. Never ails 4) I case o Bisectio method, the covergece is A. liear B. C. very slow D. quadratic 5) Uder the coditios that (A) ad (B) have opposite sigs ad a<b, the irst approimatio o oe o the roots ()=, by Regula-Falsi method is give by a ( a) b ( b) a ( b) b ( a) A. B. ( a) ( b) ( b) ( a) a ( a) b ( b) a ( b) b ( a) C. D. ( a) ( b) ( b) ( a) 6) For method o solutio o equatios o the orm () = approimatio be very close to the root ad ( ) is to A. Bolao B. Newto-Raphso C.Secet D. Chord 7) I the bisectio method o solutio o a equatio o the orm () = the covergece o the sequece o midpoits to a root o () = i a iterval (a,b) where (A)(B)< is A. Assured ad very ast B. Not assured but very ast C. Assured but very slow D. Idepedet o the sequece o poit 8) Newto-Raphso method is used or A. Solutio o algebraic or trascedetal equatio B. Itegratio o a uctio C. Dieretial o a uctio D. Solutio o a uctio 9) I the method o False positio or solutio o a equatio o the orm () = the covergece o the sequece iterates to a root o () = is A. Assured ad very ast B. Not assured but very ast C. Assured but slow D. Idepedet o the sequece o poit ). I Newto Raphso method we approimate the graph o by suitable A. Chords B.Tagets C. Secats D. Parallel ) Newto s iterative ormula or idig a root o ( ) = is ( ) ( ) A. B. ( ) ( ) C. D. ) Newto-Raphso method is also called A. Method o taget B. Method o alse positio C. Method o chord D. Method o secats ) Amog the method o solutio o equatio o the orm () = the oe which is used commoly or its simplicity ad great speed is ---method A. Secat B. Regula alsi C. Newto Rasphso D. Bolao 6HS6

14 QUESTION BANK 8 6HS6 4) The Regula Falsi method is related to at a poit o the curve A. Chord B. Ordiate C. Abscissa D. Taget 5) The Newto Raphso method is related to at a poit o the curve A. Chord B. Ordiate C. Abscissa D. Taget 6) Newto s iterative ormula or idig the square root o a positive umber N is A. i i i N B. i i i N C. i i i N D. i i i N 7) Newto s iterative ormula or idig the reciprocal o a umber N is A. N B. N C. N D. N 8) Regula- alsi method is used or A. Solutio o algebraic or trascedetal equatio B. Itegratio o a uctio C. Dieretial o a uctio D. Solutio o a uctio 9) The cube root o 4 by Newto s ormula takig is A..889 B..889 C D ) The square root o 5 by Newto s ormula takig 6 is A.7.96 B.5.96 C.6.96 D.4.96 ) I irst two approimatio ad are roots o e are ad by Regula-alsi method the is A..575 B..575 C D ) I irst two approimatio ad are roots o 4 are ad by Regula-alsi method the is A B..666 C..666 D..666 ) Newto s iterative ormula or idig the pth root o a positive umber N is A. p N p p B. p N p p C. p N p p D. p N p 4) The geeral iteratio ormula o the Regula Falsi method is A. ) ( ) ( B. ) ( ) ( C. ) ( ) ( D. ) ( ) (

15 QUESTION BANK ) I irst approimatio root o 5 is the by Newto-Raphso method is A B C D ) Newto s iterative ormula to id the value o N A. B. N N C. D. N.8 is 7) I irst approimatio root o is the by Newto-Raphso method is A..5 B..5 C..5 D..5 8) Newto s iterative ormula to id the value o N N is N N A. B. N N C. D. 9) 6. I irst two approimatio ad are roots o log 7 are.5 ad 4 by Regula- Falsi method the is A B C D ) I irst approimatio root o cos is 5 the by Newto-Raphso method is A..554 B..554 C..554 D..4 Prepared by: RAJAGOPAL REDDY N 6HS6

16 QUESTION BANK 8 SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayaavaam Road 5758 QUESTION BANK (DESCRIPTIVE) Subject with Code : (6HS6) Course & Brach: B.Tech AG Year & Sem: II-B.Tech& I-Sem Regulatio: R6. Fit the curve b y ae to the ollowig data. UNIT IV X Y [M]. A)Fit the epoetial curve o the orm y ab or the data X 4 Y B) Fit a straight lie y=a+b rom the ollowig data X 4 Y Fit a secod degree polyomial to the ollowig data by the method o least squares [M] X 4 Y B) Fit a straight lie y=a+b rom the ollowig data X Y A) Fit a Power curve to the ollowig data X Y B) Fit a secod degree polyomial to the ollowig data by the method o least squares X 4 Y 5 8 6HS6

17 QUESTION BANK 8 y ae b 5. A) Fit the curve o the orm X Y y ab B) Fit the curve o the orm or X Y A) Usig Simpso s 8 rule, evaluate 6 d B) Evaluate d takig h =. usig Trapioidal rule 7. Dividig the rage ito equal parts,id the value o 8. Evaluate d i) By trapeoidal rule ad Simpso s rule. ii) Usig Simpso s 4 9. A) Compute 7 B).Fid 8 / si rule ad compare the result with actual value. dusig Simpso s rule. [M] e d by Simpso s rule with subdivisios. log d, usig Trapeoidal rule ad Simpso s rule by sub divisios.. A) Evaluate approimately,by Trapioidal rule, ( 4 ) d by takig =. B) Evaluate e d takig h =.5 usig Simpso s rule Prepared by: RAJAGOPAL REDDY N 6HS6

18 QUESTION BANK 8 SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayaavaam Road 5758 QUESTION BANK (DESCRIPTIVE) Subject with Code : (6HS6) Course & Brach: B.Tech AG Year & Sem: II-B.Tech& I-Sem Regulatio: R6. The th A) Polyomial o. The UNIT IV order dierece o a polyomial o th th degree is degree B) polyomial o irst degree C) costat D) Zero th order dierece o a polyomial o ( ) th th degree is A) Polyomial o degree B) costat C) polyomial o irst degree D)Noe. While evaluatig a deiite itegral by Trapeoidal rule, the accuracy ca be icreased by takig umber o subitervals. A) Larger B)smaller C) Medium D)Noe 4. I Simpso s /8 rule the umber o subitervals should be A) Eve B) Odd C) Multiples o 8 D) Multiples o 5.. I Simpso s / rule the umber o subitervals should be A) Eve B) Multiples o C) Odd D) Noe 6. The ollowig ormula is used or uequal itervals o values A) Newto s orward B)Lagrage s C) Newto s backward D)Noe 7. The priciple o least squares states that A) Sum o residuals is miimum B) Sum o residuals is maimum C) Sum o squares o the residuals is miimum D) Noe 8. I y a a the secod ormal equatio by least square method is_ A) y a a B) y a a C) y a a D) Noe 9. I y=6.77,y= l(y) the Y= A).845 B).845 C).845 D).845. I y=4.77,y= l(y) the Y= A).4 B).45 C).459 D) Noe. I y=8.,y= logy the Y= A).99 B) 9.9 C).99 D) Noe. I y a b the irst ormal equatio by least square method is A) y a b B) y a b C) y a b D) Noe. I y a b c the secod ormal equatio by least square method is A) y a b c B) y a b c C) y a b c D) y a b c 6HS6

19 QUESTION BANK 8 y a b 4. I c the third ormal equatio by least square method is A) y a b c B) y a b c a b c y a b c C) y D) 5. I Simpso s b rule state that ( ) d = A) [( y y ) ( y y... y )] a h B) h y y ) ( y y... y )] 6. The value o [( C) h [( y y ) ( y y4...) 4( y y...)] D) Noe / ( ) d by Simpso s / rule(take =4) is A).69 B).5 C) -.69 D) Noe 7. I y a b c the secod ormal equatio by least square method is A) y a b c B) y a b c C) y a b c D) y a b c 8. I i 5, yi, i yi, i 55, 4 ad y a a The A). B).5 C). D) 9. I y a a a the secod ormal equatio by least square method is A) y a a a C) y a a a 5, yi, i yi, i 55, 4 B) y a a a D) y a a a. I i 5 ad y a a The A). B).5 C). D). The Epoetial curve is.. b b b A) y a B) y a C) y ae D) Noe. The power curve is.. b b A) y a B) y ab C) y a D) Noe. I y a b the secod ormal equatio by least square method is A) y a b B) y a b C) y a b D) Noe 4. I y a b the irst ormal equatio by least square method is A) y a b B) y a b C) y a b D) Noe 5. I Simpso s /8 rule the umber o subitervals should be A) Eve B) Odd C) Multiples o D) Noe a a 6HS6

20 QUESTION BANK 8 b 6. By Trapeoidal rule, ( ) d a h A) [( y y ) ( y y... y )] h C) [( y y ) ( y y... y )] h B) [( y y ) ( y y... y )] h D) [( y y ) ( y y... y )] 7. I Simpso s rule state that b ( ) a d = A) h [( y y ) ( y y4...) 4( y y...)] B) h [( y y ) ( y y... y )] h C) [( y y ) ( y y... y )] D) Noe 8. I the geeral quadrature ormula = gives A) Trapeoidal rule B) Simpso s rule C) Simpso s rule D) Weddle s rule 9. The value o / d by Trapeoidal rule(take =4) is A).69 B).5 C) -.69 D) Noe d. The value o by Simpso s rule (take =4) is A).6854 B).7854 C).8854 D) The value o / ( ) d by Simpso s / rule(take =4) is A).69 B).5 C) -.69 D) Noe. The value o d by Trapeoidal rule (take =4) is A).5 B).5 C).5 D).5. Equatio o the straight is A) y a b B) y a b C) y a b D) b y a the irst ormal equatio is 8 y a b 4. I log y (=No.o poits give) A) a b B) log a b C) a b log D) log a b log 5. I Simpso s 8 b rule state that ( ) d = a A) h [( y y ) ( y y y... y ) ( y y y... y ) B) h [( y y ) ( y y4...) 4( y y...)] C) h [( y y ) ( y y4...) 4( y y...)] D) Noe 6HS6

21 QUESTION BANK 8 6. I y=9.,y= logy the Y= A).9685 B).9685 C).9685 D) I simpso s rule the umber o sub itervals should be A) eve B)odd C)multiple o D) Noe 8. I simpso s rule the umber o ordiates should be ` [ ] A) Eve B) odd C) multiple o D) Noe 9. I simpso s 8 rule the umber o sub itervals should be A) Eve B) odd C) multiple o D) Noe 4. The value o / ( ) d by simpso s / rule(take =4) is A).69 B).589 C).456 D) 56 Prepared by: RAJAGOPAL REDDY N 6HS6

22 QUESTION BANK 8 SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayaavaam Road 5758 QUESTION BANK (DESCRIPTIVE) Subject with Code : (6HS6) Course & Brach: B.Tech AG Year & Sem: II-B.Tech& I-Sem Regulatio: R6 UNIT V. a ) Tabulate y (.), y (.), ad y (.) usig Taylor s series method give that y y ad y() = B) Fid the value o y or =.4 by Picard s method give that dy d = +y, y()=. Usig Taylor s series method id a approimate value o y at =. or the D.E y - y = e, y() =. Compare the umerical solutio obtaied with eact solutio.[m] y y. A)Solve, give y ()= id y(.) ad y(.) by Taylor s series method y B) Obtai y(.) give y,y()= by Picard s method. y 4. A) Give that 5. dy d B) Solve by Euler s method =+y ad y () = compute y(.),y(.) usig Picard s method dy y d give y() = ad id y(). A)Usig Ruge-Kutta method o secod order, compute y(.5) rom y y y()=, takig h=.5 B) Solve umerically usig Euler s method y ' y, y()=. Fid y(.) ad y(.) 6. A)Usig Euler s method, solve umerically the equatio y =+y, y()= B) Solve y = y-, y () = by Picard s method up to the ourth approimatio. Hece id the value o y (.), y (.). 7. A) Use Ruge- kutta method to evaluate y(.) ad y(.) give that y =+y, y()= ' B) Solve umerically usig Euler s method y y, y(). Fid y(.)ad y(.) 6HS6

23 QUESTION BANK 8 8. A)Usig R-K method o 4 th dy y order, solve, y()= Fid y(.) ad y(.4) [6M] d y B)Obtai Picard s secod approimate solutio o the iitial value problem dy, y [4M] d y 9. Usig R-K method o 4 th dy order id y(.),y(.) ad y(.) give that y, y d. A)Fid y(.) ad y(.) usig R-K 4 th order ormula give that y = -y ad y()= dy B) Usig Taylor s series method, solve the equatio y or =.4 give that d y = whe =. Prepared by: RAJAGOPAL REDDY N 6HS6

24 QUESTION BANK 8 SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayaavaam Road 5758 QUESTION BANK (DESCRIPTIVE) Subject with Code : (6HS6) Course & Brach: B.Tech AG Year & Sem: II-B.Tech& I-Sem Regulatio: R6 UNIT V ) Successive approimatios are used i A) Mile s method B) Picard s method C) Taylor series method D) oe ) Which o the ollowig i a step by step method: A) Taylor s series B) Adam s bashorth C)Picard s D) oe ) Ruge-kutta method is sel startig method: A) true B) alse C) we ca t say D) oe 4) The secod order Ruga-kutta ormula is A) Euler s method B) Newto s method C) Modiied Euler s method D) oe 5) Euler s th term ormula is A) y = y + h(, y ) B) y + = y + h(, y ) C) y = y + h(, y ) D) oe 6) Which o the ollowig is best or solvig iitial value problems. A) Euler s method B) Modiied Euler s method C) Taylor s series method D) Ruge-kutta method o order 4 7) To obtai reasoable accuracy value i Euler s method, we have to h value is A) Small B) large C) D) oe 8) I coditios are speciied at the iitial poit, the it is called A) Iitial value problem B) ial value problem C) Boudary value problem D) Noe 9) I coditios are speciied at two or more poits, the it is called A) Iitial value problem B) ial value problem C) Boudary value problem D) Noe ) The irst order Ruga-kutta ormula is A) Euler s method B) Newto s method C) Modiied Euler s method D) Noe ) The secod order Ruge-Kutta ormula is y = A) y +(k + k) B) y - (k + k) C) y + (k + k) D) y - (k + k) ) The th dierece o a th degree polyomial is A) Costat B) Zero C) oe D) Noe ) Successive approimatios used i method A) Euler s B) Taylor s C) Picard s D) R-K 4) The taylor s or () =log (+) is A) B) + -. C) Both a ad b D) Noe 6HS6

25 QUESTION BANK 8 5) Solvey = + y, y() =, id y = y(.) by usig Euler s method A). B).6 C). D).86 6) The R-K method is a.. method A) Picard s method B) Euler s method C) Mile s method D) sel- startig method 7) Usig Euler s method y = y y+, y()= ad h=.give y=. A). B). C). D). 8) Usig Euler s method y = y, y()= the the picard s method the value o y+ y () = A) +log(+) B) -+log(+) C) +log(+) D) Noe 9) I dy d y () is A).95 B).95 C).95 D) Noe ) Euler s irst approimatio ormula is A) y = y + h(, y ) B) y = y + h(, y ) C) y = y + h(, y ) D) y = y + h(, y ) ) Secod order R-K Method ormula is A) y = y + (k + k ) B) y = y + (k 4 + 4k + k ) C) y = y + 6 (k + k ) D) y = y + (k + k ) dy ) The itegratig actor o y d A) e B) C) D) e ) The secod order Ruge-Kutta ormula is y = A) y +(k + k) B) y - (k + k) C) y + (k + k) D) y - (k + k) 4) Usig Euler s method y = y,y()= ad h=.give y=. y+ e A). B). C). D). 5) Ruge-kutta method is sel startig method: A) False B) we ca t say C) True D) Noe dy 6) The itegratig actor o y d A) e B) e C) e D) e 7) Usig Euler s method y = y,y()= ad h=.give y=. y+ A). B). C). D). 8) I dy = -y ad y()= the by Picard s method the value o d y () is A).95 B) -.95 C).95 D) Noe ' 9) I y y, y by Euler s method the value o y. is A).9 B). C) - D) -.9 dy ) I y, y the by Picard s method the value o y is d A) B) C) D) e 6HS6

26 QUESTION BANK 8 dy y ) The itegratig actor o d A) B) log C) D) dy y ) I, y,ad h=. the the value o i order R-K method is d y A) B). C). D). ) Usig Euler s method y = y,y()= ad h=. give y=. y+ A). B). C). D). dy d 4) I y, y k th 4 e, the by Picard s method the value o y () is. A) B) C) D) dy y 5) The itegratig actor o d A) B) C) D) e 6) The Third order R-K ormula is.. A) y y k k k B) y y k 4k k 6 6 C) y y k 4k k D) y y k k 4k 6 6 7) Usig Euler s method y = y y+,y()= ad h=.4give y=. A).4 B).4 C).4 D).4 8) I dy = -y ad y()= the by Picard s method the value o d y (.) is A).7 B) -.7 C).8 D) Noe y y, y by Euler s method the value o. ' 9) I y is A).9 B). C) - D) dy y, y, the by Picard s method the value o y () is. d A) B) C) D) 4) I Prepared by: RAJAGOPAL REDDY N 6HS6